Spherical Denoising via Toroidal 2D Mapping
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Solution Overview
Problem
Current graphics technologies face challenges in applying deep convolutional neural networks (CNNs) for denoising spherical light information due to the different topology of spherical signals compared to plane signals, which leads to distortion and discontinuities when trying to overlay a grid on a sphere.
Innovation Solution
Converting 3D spherical light measurements into 2D measurements by creating multiple copies and stitching them together in a toroidal configuration, allowing for denoising using machine learning implementations like CNNs, which results in rotationally invariant and distortion-free light measurements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a grid is overlaid on a sphere to apply CNN denoising, then denoising can be performed using machine learning, but distortion and discontinuities occur due to topological differences between spherical and planar signals
Solution Approach 1:
The patent converts the spherical signal from 3D space to a 2D planar representation by creating multiple copies of the spherical signal and stitching them together in a toroidal configuration. This dimensionality transformation allows CNNs to operate on the spherical data while preserving its topological properties, avoiding distortion and discontinuities that would occur with direct spherical-to-planar mapping.
Solution Approach 2:
The spherical signal is divided into multiple copies, each representing a different view or projection of the spherical data. These segmented copies are then processed individually and stitched together to form the final toroidal representation, allowing the CNN to process each segment separately while maintaining overall spherical integrity.
2Measurement precision
If high-resolution spherical light measurements are captured, then accuracy is improved, but the number of samples required becomes prohibitively large
Solution Approach 1:
The patent creates multiple copies of the spherical light measurement data and stitches them together in a toroidal configuration. This copying approach allows the system to achieve high-resolution measurements by combining information from multiple lower-resolution copies, reducing the total number of samples needed compared to capturing a single high-resolution spherical measurement directly.
3Productivity
If CNNs are applied directly to spherical data, then denoising can be performed, but the different topology causes the grid overlay to fail
Solution Approach 1:
The patent transforms spherical data into a 2D toroidal representation that is topologically compatible with planar grid structures used by CNNs. This transformation maintains the essential spherical properties while presenting the data in a format that CNNs can process efficiently, resolving the topological incompatibility between spherical geometry and planar convolutional operations.
Data Source
AI summary
In order to perform denoising on a three-dimensional (3D) spherical measurement of light (such as spherical irradiance probe information or the results of a 3D gonioreflectometry capture), the 3D spherical measurement of light is converted to a two-dimensional (2D) measurement by creating multiple copies of the 3D spherical measurement of light, determining a two-dimensional sub-domain (e.g., a rectangular sub-domain) for each of the multiple copies, and stitching the plurality of two-dimensional sub-domains together in a toroidal configuration. Denoising may then be performed on this 2D measurement via a machine learning implementation or other means. This may result in more accurate 3D spherical light probes that require fewer light measurement samples to generate accurate light measurements.